Pressure dependence of the angular correlation of positron-annihilation radiation in sodium

Abstract

The pressure dependence of the angular correlation of positron-annihilation radiation in sodium was measured in the range from 4 to 68 kbar. Below 55 kbar the measured value of 8+ was consistent with the predictions of the nearly-free-electron model. Above 55 kbar, 8z deviated from the nearly-free-electron model, indicating that above 55 kbar the electronic structure of sodium metal may no longer be free-electron-like. The percentage pf core annihilations varied smoothly from 30% at 4 kbar to 42% at 68 kbar. As pointed out by Kubica and Stott this incr~a= in the core-annihilation percentage with pressure allows the measurements of the pressure dependence of the positron lifetime in sodium made by MaeKenxie, LeBlanc, and McKee to be explained. The pressure dependence of the enhancement of the electrons at the positron was also ex~~ined. Reasonable absolute agreement with the theories of Kahana and Carbotte was observed, but the variation in the ratios of the enhancement coe%cients with pressure was not in agreement with the theoretical predictions.

Hyperbolic Limit Sets of Evolutionary Equations and the Galerkin Method

“…Table 2 shows the experimental results of several groups. Again, at rs = 2 (for aluminium), the agreement of our result with the experimental results of Gustafson and Willenberg (1976) is remarkable. Other recent experiments for A1 (Mader er al 1976, Okada et a1 1976 are also consistent with the present and Kahana's theory.…”

“…For sodium, several measurements have been performed, of which the results of Gustafson and Willenberg (1976) are closest to our theoretical estimate; but even here a fairly large discrepancy remains. For rubidium and caesium our results are consistent with the measurement by Arias-Limonta and Varlashkin (1970), but the rubidium results obtained by Kim and Stewart (1975) are markedly different.…”

“…in measurements involving the application of essentially the same techniques as those mentioned above, Arias-Limonta and Varlashkin (1970) observed no essential dependence on P of E ( P ) , meaning that b/a and cia are almost zero for rubidium (r, = 5.2) and caesium (r5 = 5.6). Another somewhat contradictory result was obtained by Gustafson and Willenberg (1976) who compressed sodium metal to vary the densit] parameter ri. In their experimental results the values of bia and c/a are on average in accordance with Kahana's result, but both the ratios appear to be steeply descending functions of rz around 3.43.9 in marked contrast to Kahana's prediction.…”

“…' Kim and Stewart (1975) ' Gustafson and Willenberg (1976) then It is possible to determine the behaviour of in the high-density limit rs + 0. In the Appendix we show that g(rs) -&(In r,)' + smaller terms.…”

“…For Mg (r, = 2.65) Kahana's prediction is ( b + c)/a 'c 0.32, and ours is about 0.24, which both seem to be too low. Another unexplained feature is the dependence on pressure of the ratios b/a, c,'a for sodium (Gustafson and Willenberg 1976). Because of the very strong dependence of (b + c)/a on the density parameter rs in the region 3 4 3 .…”